Problem: Ikta has an extraordinary feeling for undirected graphs. Ikta likes the undirected graph G and its two-point s, t pair (G, s, t) that has the greatest "beauty". The "beauty" of a pair (G, s, t) is the edge e = \\ {u, v \\} (u and v are two different points of G), and the shortest path from s to t in G. Is the number of things whose length is greater than the length of the shortest path from s to t in the undirected graph with g plus e.

Your job is to write a program that seeks its "beauty" given a pair (G, s, t).



Input

The input is given in the following format.

> N M s t
> x1 y1
> ...
> xi yi
> ...
> xM yM
>

First, the number of vertices, the number of edges, and the integers N, M, s, t representing the two vertices of the undirected graph are input. From the 2nd line to the M + 1th line, two vertices connected by edges are input. (However, let the set of G vertices be \\ {1, ..., N \\}.)

Constraints

Each variable being input satisfies the following constraints.

* 2 ≤ N ≤ 100,000
* 1 ≤ M ≤ 300,000
* 1 ≤ s, t, xi, yi ≤ N
* Different from s and t
* Guaranteed to reach t from s

Output

When the given graph is G, output the "beauty" of the set (G, s, t) in one line.

Examples

Input

3 2 1 3
1 2
2 3


Output

1


Input

9 8 7 8
2 6
4 9
8 6
9 2
3 8
1 8
8 5
7 9


Output

7


Input

4 3 1 4
1 2
3 4
4 1


Output

0


Input

9 7 8 9
9 6
6 5
3 6
3 7
2 5
8 5
1 4


Output

2

Solution (in CPP):

Solution:
#include <iostream>
#include <fstream>
#include <cassert>
#include <typeinfo>
#include <vector>
#include <stack>
#include <cmath>
#include <set>
#include <map>
#include <string>
#include <algorithm>
#include <cstdio>
#include <queue>
#include <iomanip>
#include <cctype>
#include <random>
#include <time.h>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<char> vc;
typedef vector<vc> vvc;
typedef vector<string> vs;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<P,int> pip;
typedef vector<pip> vip;
const int inf=1<<28;
const ll INF=1ll<<60;
const double pi=acos(-1);
const double eps=1e-8;
const ll mod=1e9+7;
const int dx[4]={0,1,0,-1},dy[4]={1,0,-1,0};

class Graph{
	private:
	int V;
	vvi List;
	vi DIJ(int s){
		priority_queue<P> que;
		vi d(V,inf);
		d[s]=0;
		que.push({0,s});
		while(!que.empty()){
			P p=que.top();
			que.pop();
			int v=p.second;
			if(d[v]<-p.first) continue;
			for(int i=0;i<List[v].size();i++){
				int F=List[v][i];
				if(d[F]>d[v]+1){
					d[F]=d[v]+1;
					que.push({-d[F],F});
				}
			}
		}
		return d;
	}
	public:
	Graph(int v){
		V=v;
		List=vvi(v);
	}
	void add_edge(int s,int t){
		List[s].push_back(t);
		List[t].push_back(s);
	}
	ll solve(int s,int t){
		vi ds=DIJ(s),dt=DIJ(t);
		sort(dt.begin(),dt.end());
		ll res=0,d=ds[t]-2;
		for(int i=0;i<V;i++){
			res+=upper_bound(dt.begin(),dt.end(),d-ds[i])-lower_bound(dt.begin(),dt.end(),d-ds[i]);
		}
		return res;
	}
};

int n,m,s,t;

int main(){
	cin>>n>>m>>s>>t;
	Graph g(n);
	for(int i=0;i<m;i++){
		int u,v;
		cin>>u>>v;
		g.add_edge(u-1,v-1);
	}
	cout<<g.solve(s-1,t-1)<<endl;
}